<p>One related result to your problem:</p><p>&nbsp; The sample path of Brownian motion B(t) is of unbounded variation on every interval of t. </p><p>I guess \int_{0}^{t} B_s ds&nbsp; must be of unbounded variation also. I don't know how to prove it at this moment. </p><br>holdser
&nbsp;金钱&nbsp;+1
&nbsp;奖励&nbsp;2009-5-30 22:59:31

B_t的轨道是连续的，而且在[0,t]区间上几乎每条路径都是有限的. f(t)=\int_0^t B_s ds 是对一个连续函数的积分，所以是可导的，而且导数是有限的，所以是有界变差的。 证毕。<br>holdser
&nbsp;金钱&nbsp;+5
&nbsp;奖励帮助解决会员问题&nbsp;2009-5-30 22:59:09

thanks vertigo, you gave the right answer~